Author : Francoise Chatelin
Publisher : SIAM
Page : 482 pages
File Size : 17,72 MB
Release : 2011-05-26
Category : Mathematics
ISBN : 0898719992
Originally published: New York: Academic Press, 1983.
Author : M Thamban Nair
Publisher : World Scientific
Page : 264 pages
File Size : 27,21 MB
Release : 2009-05-05
Category : Mathematics
ISBN : 981446967X
Many problems in science and engineering have their mathematical formulation as an operator equation Tx=y, where T is a linear or nonlinear operator between certain function spaces. In practice, such equations are solved approximately using numerical methods, as their exact solution may not often be possible or may not be worth looking for due to physical constraints. In such situations, it is desirable to know how the so-called approximate solution approximates the exact solution, and what the error involved in such procedures would be.This book is concerned with the investigation of the above theoretical issues related to approximately solving linear operator equations. The main tools used for this purpose are basic results from functional analysis and some rudimentary ideas from numerical analysis. To make this book more accessible to readers, no in-depth knowledge on these disciplines is assumed for reading this book.
Author : Amnon Pazy
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 46,27 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461255619
Since the characterization of generators of C0 semigroups was established in the 1940s, semigroups of linear operators and its neighboring areas have developed into an abstract theory that has become a necessary discipline in functional analysis and differential equations. This book presents that theory and its basic applications, and the last two chapters give a connected account of the applications to partial differential equations.
Author : Tosio Kato
Publisher : Springer Science & Business Media
Page : 610 pages
File Size : 14,32 MB
Release : 2013-06-29
Category : Mathematics
ISBN : 3662126788
Author : David Eric Edmunds
Publisher : Oxford University Press
Page : 610 pages
File Size : 21,40 MB
Release : 2018
Category : Mathematics
ISBN : 0198812051
This book is an updated version of the classic 1987 monograph "Spectral Theory and Differential Operators".The original book was a cutting edge account of the theory of bounded and closed linear operators in Banach and Hilbert spaces relevant to spectral problems involving differential equations. It is accessible to a graduate student as well as meeting the needs of seasoned researchers in mathematics and mathematical physics. This revised edition corrects various errors, and adds extensive notes to the end of each chapter which describe the considerable progress that has been made on the topic in the last 30 years.
Author : Lloyd N. Trefethen
Publisher : Princeton University Press
Page : 634 pages
File Size : 49,47 MB
Release : 2005-08-07
Category : Mathematics
ISBN : 9780691119465
Pure and applied mathematicians, physicists, scientists, and engineers use matrices and operators and their eigenvalues in quantum mechanics, fluid mechanics, structural analysis, acoustics, ecology, numerical analysis, and many other areas. However, in some applications the usual analysis based on eigenvalues fails. For example, eigenvalues are often ineffective for analyzing dynamical systems such as fluid flow, Markov chains, ecological models, and matrix iterations. That's where this book comes in. This is the authoritative work on nonnormal matrices and operators, written by the authorities who made them famous. Each of the sixty sections is written as a self-contained essay. Each document is a lavishly illustrated introductory survey of its topic, complete with beautiful numerical experiments and all the right references. The breadth of included topics and the numerous applications that provide links between fields will make this an essential reference in mathematics and related sciences.
Author : P.D. Hislop
Publisher : Springer Science & Business Media
Page : 331 pages
File Size : 49,29 MB
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 146120741X
The intention of this book is to introduce students to active areas of research in mathematical physics in a rather direct way minimizing the use of abstract mathematics. The main features are geometric methods in spectral analysis, exponential decay of eigenfunctions, semi-classical analysis of bound state problems, and semi-classical analysis of resonance. A new geometric point of view along with new techniques are brought out in this book which have both been discovered within the past decade. This book is designed to be used as a textbook, unlike the competitors which are either too fundamental in their approach or are too abstract in nature to be considered as texts. The authors' text fills a gap in the marketplace.
Author : David Gottlieb
Publisher : SIAM
Page : 167 pages
File Size : 41,74 MB
Release : 1977-01-01
Category : Technology & Engineering
ISBN : 0898710235
A unified discussion of the formulation and analysis of special methods of mixed initial boundary-value problems. The focus is on the development of a new mathematical theory that explains why and how well spectral methods work. Included are interesting extensions of the classical numerical analysis.
Author : Lloyd N. Trefethen
Publisher : SIAM
Page : 179 pages
File Size : 25,91 MB
Release : 2000-07-01
Category : Mathematics
ISBN : 0898714656
Mathematics of Computing -- Numerical Analysis.
Author : Philippe G. Ciarlet
Publisher : SIAM
Page : 847 pages
File Size : 23,37 MB
Release : 2013-10-10
Category : Mathematics
ISBN : 1611972582
This single-volume textbook covers the fundamentals of linear and nonlinear functional analysis, illustrating most of the basic theorems with numerous applications to linear and nonlinear partial differential equations and to selected topics from numerical analysis and optimization theory. This book has pedagogical appeal because it features self-contained and complete proofs of most of the theorems, some of which are not always easy to locate in the literature or are difficult to reconstitute. It also offers 401 problems and 52 figures, plus historical notes and many original references that provide an idea of the genesis of the important results, and it covers most of the core topics from functional analysis.
